Answer
$(f \circ g)(x) = 2^{x^2}$,
$(g \circ f)(x) = 2^{2x}$.
Domains: $\mathbb{R}$
Work Step by Step
We have the composite functions:
$(f \circ g)(x) = f(g(x)) = f(x^{2}) = 2^{x^2}$,
$(g \circ f)(x) = g(f(x)) = g(2^{x}) = (2^{x})^{2} = 2^{2x}$.
The domains $D_f, D_g$ are the same and equal to $\mathbb{R}$.
Similarly, the domains of the compositions $f \circ g$ and $g \circ f$ are the same and equal to $\mathbb{R}$.
